{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:NU2S7BPVMQVDLMST7YHMURNCQ3","short_pith_number":"pith:NU2S7BPV","schema_version":"1.0","canonical_sha256":"6d352f85f5642a35b253fe0eca45a286c038c3781fb7918da3212d9fb90b3444","source":{"kind":"arxiv","id":"1207.7153","version":2},"attestation_state":"computed","paper":{"title":"Containment problem for points on a reducible conic in $\\mathbb{P}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Annika Denkert, Mike Janssen","submitted_at":"2012-07-31T03:17:30Z","abstract_excerpt":"Given an ideal $I$ in a Noetherian ring, one can ask the containment question: for which $m$ and $r$ is the symbolic power $I^{(m)}$ contained in the ordinary power $I^r$? C. Bocci and B. Harbourne study the containment question in a geometric setting, where the ideal $I$ is in a polynomial ring over a field. Like them, we will consider special geometric constructs. In particular, we obtain a complete solution in two extreme cases of ideals of points on a pair of lines in $\\mathbb{P}^2$; in one case, the number of points on each line is the same, while in the other all the points but one are o"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1207.7153","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-07-31T03:17:30Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"0ce3531b102d83a0757265d2bbc41ce677937dbed3dc1ec1be443c784596b50f","abstract_canon_sha256":"4435bcaa8edc74dc8e92c06cd163e4ad5ce262533abd0515513cf722e94cbb09"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:43.809289Z","signature_b64":"85kwEv91zyBljzMv4XtJRdJynOr/amUGkED+KwngVkcWomcURpvzfade2tU3IuEz7qeWV0kzKXOunweiQQNrCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d352f85f5642a35b253fe0eca45a286c038c3781fb7918da3212d9fb90b3444","last_reissued_at":"2026-05-18T03:25:43.808497Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:43.808497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Containment problem for points on a reducible conic in $\\mathbb{P}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Annika Denkert, Mike Janssen","submitted_at":"2012-07-31T03:17:30Z","abstract_excerpt":"Given an ideal $I$ in a Noetherian ring, one can ask the containment question: for which $m$ and $r$ is the symbolic power $I^{(m)}$ contained in the ordinary power $I^r$? C. Bocci and B. Harbourne study the containment question in a geometric setting, where the ideal $I$ is in a polynomial ring over a field. Like them, we will consider special geometric constructs. In particular, we obtain a complete solution in two extreme cases of ideals of points on a pair of lines in $\\mathbb{P}^2$; in one case, the number of points on each line is the same, while in the other all the points but one are o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.7153","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1207.7153","created_at":"2026-05-18T03:25:43.808620+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.7153v2","created_at":"2026-05-18T03:25:43.808620+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.7153","created_at":"2026-05-18T03:25:43.808620+00:00"},{"alias_kind":"pith_short_12","alias_value":"NU2S7BPVMQVD","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"NU2S7BPVMQVDLMST","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"NU2S7BPV","created_at":"2026-05-18T12:27:16.716162+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NU2S7BPVMQVDLMST7YHMURNCQ3","json":"https://pith.science/pith/NU2S7BPVMQVDLMST7YHMURNCQ3.json","graph_json":"https://pith.science/api/pith-number/NU2S7BPVMQVDLMST7YHMURNCQ3/graph.json","events_json":"https://pith.science/api/pith-number/NU2S7BPVMQVDLMST7YHMURNCQ3/events.json","paper":"https://pith.science/paper/NU2S7BPV"},"agent_actions":{"view_html":"https://pith.science/pith/NU2S7BPVMQVDLMST7YHMURNCQ3","download_json":"https://pith.science/pith/NU2S7BPVMQVDLMST7YHMURNCQ3.json","view_paper":"https://pith.science/paper/NU2S7BPV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.7153&json=true","fetch_graph":"https://pith.science/api/pith-number/NU2S7BPVMQVDLMST7YHMURNCQ3/graph.json","fetch_events":"https://pith.science/api/pith-number/NU2S7BPVMQVDLMST7YHMURNCQ3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NU2S7BPVMQVDLMST7YHMURNCQ3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NU2S7BPVMQVDLMST7YHMURNCQ3/action/storage_attestation","attest_author":"https://pith.science/pith/NU2S7BPVMQVDLMST7YHMURNCQ3/action/author_attestation","sign_citation":"https://pith.science/pith/NU2S7BPVMQVDLMST7YHMURNCQ3/action/citation_signature","submit_replication":"https://pith.science/pith/NU2S7BPVMQVDLMST7YHMURNCQ3/action/replication_record"}},"created_at":"2026-05-18T03:25:43.808620+00:00","updated_at":"2026-05-18T03:25:43.808620+00:00"}